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Modified quadrature formula for integrand with nearby poles

✍ Scribed by Yue-Kuen Kwok; Kin-Kiu Tam

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
179 KB
Volume
6
Category
Article
ISSN
0893-9659

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✦ Synopsis

The conventional trapezoidal approximation for the numerical evaluation of the integral formula for the Dirichlet problem inside the unit disc becomes highly inaccurate when the point of evaluation is approaching the boundary of the circular domain. This is due to the presence of two nearby poles of the integrand function near the interval of integration. A modified quadrature formula is derived using the generalized Residue Theorem which provides much accurate numerical approximation of the integral formula compared with the trapezoidal approximation. Error estimates of the proposed numerical quadrature are also presented.

πŸ“œ SIMILAR VOLUMES

Modified quadrature formulas for functio
Modified quadrature formulas for functions with nearby poles
✍ Frank G. Lether πŸ“‚ Article πŸ“… 1977 πŸ› Elsevier Science 🌐 English βš– 375 KB

This paper is concerned with the numerical integration of functions with poles near the interval of integration. A method is given for modifying known quadrature rules, to obtain rules which are exact for certain classes of rational functions.